Find the value of x.
a. 2
b. 4
c. 6
d. 8

Explanation:

Use the Pyhagorean theorem

leg² + leg² = hypotenuse²

We have leg = x, leg = x - 2 and hypotenuse = √20. Substitute:

x² + (x - 2)² = (√20)²

use (a - b)² = a² + 2ab + b² and (√a)² = a

x² + x² - 2(x)(2) + 2² = 20

2x² - 4x + 4 = 20                subtract 20 from both sides

2x² - 4x - 16 = 0              divide both sides by 2

x² - 2x - 8 = 0

x² + 2x - 4x - 8 = 0

x(x + 2) - 4(x + 2) = 0

(x + 2)(x - 4) = 0 ⇔ x + 2 = 0 ∨ x - 4 = 0

x + 2 = 0           subtract 2 from both sides

x = -2 < 0

x - 4 = 0           add 4 to both sides

x = 4

2686-2181 bce-- "egyptian civilization developed along the nile river in large part because the river’s annual flooding ensured reliable, rich soil for growing crops."

1069-664 bce-- "ancient egyptians developed wide-reaching trade networks along the nile, in the red sea, and in the near east."

the growing interconnectedness of the world through communication, trade, and the exchange of ideas is an important theme in the history of the 20th and 21st centuries.

explanation: